Wave transmission network



- June 16; 1936- I 0515 2,044,047

WAVE TRANSMISSION NETWORK Filed Jan. 10,' 1955 8 Sheets-Sheet 1 R, 2 R R},

FIG. 8 9mm lNl ENTOR S BOB/S AT TORNE Y June 16, 1936. 5 BOBIS 2,044,047

WAVE TRANSMISSION NETWORK 7 Filed Jan. 10, 1935 8 Sheets-Sheet 2 2 I 4 /N VENTOR S. BOB/S ATTbR/VEV Filed Jan. 10, 1955 8 Sheets-Sheet 4 5 4 6 6 k 5 R q FREQUENCY lNl ENrOP $.BOB/S BY A TTORNE V June 16, s Bls 2,044,047

WAVE TRANSMISSION NETWORK Filed Jan. 10, 1935 8 Sheets-Sheet 5 FIG. /2 FIG. /3

INI ENTOR 's. BOB/5 i-vM ATTORNEY June 16, 1936. s. BOBIS 2,044,047

WAVE TRANSMISSION NETWORK Filed Jan. 10, 1955 8 Sheets-Sheet 6 1 RI 2 2 a a v vVVVV INVENTOR By S. BOB/.5,-

A TTORNE V 16, s BOBlS WAVE TRANSMI S S ION NETWORK 10, 1955 8 Sheets -sheet 7 Filed Jan.

FIG. /9

M/l/ENTOR S. BOB/S I FREQUENCY EORYDEWRRY ATTORNEY June 16, 1936. 5 BOBIS 2,044,047

WAVE TRANSMISSION NETWORK Filed Jan. 10, 1955 8 Sheets-Sheet s INVENTOR ATTORNEY 5. BOB/S Patented June 16, 1 936 WAVE TRANSMISSION NETWORK Stephen Bobis, New York, N. Y., assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application January 10, 1935, Serial No. 1,140 19 Claims. (01. 178-44) This invention relates to selective wave transmission networks having a constant non-reactive characteristic impedance at all frequencies, and more particularly to networks of this type which have a plurality of transmission channels.

may be provided for the various channels and the attenuation at the cross-over points between adjacent channels may be made any desired amount. In certain cases it may be found desirable to increase the attenuation in the individual An object of the invention is to separate sigchannels by adding auxiliary filters which are nal currents into a plurality of separate frequency effective in those channels only. In a modified channels. form of the bridged-T network no so-called ideal Another object is to reduce the reflection efiects transformer is required. In another form of the at the junction points between wave filters and invention it is shown how to build a filter having 10 their associated terminal loads. an attenuation characteristic which maintains a A further object is to increase the attenuation consistently high value at all frequencies outside at the cross-over points between the separate of the transmission band.

channels of a multi-channel wave filter, The nature of the invention will be more fully A feature of the invention is a selective wave unde s od f e following detailed descripl5 transmission network of the lattice or bridgedtion and by refe ence to the ac pa y W- T type having at least two impedance branches ings, o Wh ch: each of which comprises a plurality of partial Fig. 1 shows diagrammat c l y t e network of networks. 7 the invention in the lattice form;

In carrier communication systems, the prob- Fig. 2 is a diagrammatic representation of the lem frequently arises of separating signal curnetwork of the invention in the bridged-T form; rents into a number of separate frequency bands. 3 is a modified form of the b d e -T net- In order to minimize reflection effects the selec- Work of tive networks employed for this purpose should 4 is a diagrammatic Circuit showing how have a characteristic impedance which matches t e pu s of e a t tw of 2 may the connectedloadimpedances. In systems of this be Combined to provide a mu ti-channel selective type, the load impedances are usually constant network; resistances and, therefore, the characteristic im- 5 shows how the network of 4 y be pedance of the filters employed should also be modified by the addition Of three-winding transnon-reactive and constant with frequency. formers so that a each pair of m na s the so In accordance with the present invention there Characteristic impedance Will be a Constant p re is provided a selective wave transmission network resistance a all frequencies; which may have any desired number of separate F g. 6 is a modification of the network shown transmission channels and. the characteristic imin Fig. 4 in which some of the partial networks pedance of which at each pair of terminals is are two-terminal instead of four-terminal struc- 35 a constant pure resistance at all frequencies. The tures network is of the lattice or bridged-T type and 7 i a pe fic embodiment of the network comprises a pair of impedance branches which of Fig. 1 in a low-pass filter the attenuation of are adapted to determine the transmission charwhich at all frequencies outside of the transmisacteristics of the network. Each impedance ign ba is i t i d t a high value; a c is made p of a plurality of Pa t Fig. 8 represents the impedance of the partial Wo ks Wh h may Co s of any number of filters in the line branch of the network of Fig. 7; ponent sections. These partial networks may be Fig 9 shows a typical attenuation charactereither two-terminal or four-termmal structures istic obtainable with the network of Fig 7;

and g f P of reactances or may also Fig. 10 is a' specific embodiment of the network 00mm ise dissipative impedance branches. When of Fig. 5 in a multi charm e1 ban ass filter; the partial networks are properly chosen filters, Fig 11 gives representative attenuation char the structure as a whole will provide a plurality of Separate transmission channels having a chm aCteIlStlCS for the various channels of the netacteristic impedance at each pair of terminals Work of F 10;

which is a constant pure resistance at all frequencies. Any desired number of channels may be obtained simply by increasing the number of partial networks.

A great variety of attenuation characteristics 50 Fig. 12 is a diagrammatic representation of the transmission channels obtainable in the network of Fig. 10;

Fig. 13 shows diagrammatically how the attenuation of the individual channels may be increased by the addition of auxiliary filters effective only in the individual channels;

Fig. 14 shows the network of Fig. 10 modified in accordance with the general form shown in Fig. 4;

Fig. 15 is a multi-channel band-pass structure following the modified bridged-T form of Fig. 3;

Fig. 16 shows how the network of Fig. 15 may be modified when it is not required that the characteristic impedance be a constant pure resistance at each pair of terminals;

Fig. 17 is a specific embodiment of the network of Fig. 6 when the auxiliary partial networks contain dissipative impedance branches;

Fig. 18 represents the impedance of the partial networks in the bridging branch of the network of Fig. 17;

Fig. 19 shows typical attenuation characteristics obtainable with the wave filter of Fig. 1'1;

Fig. 20 is a specific embodiment of a network in accordance with Fig. 4 when each impedance branch consists of only a single partial network;

Fig. 21 shows how the partial network in the bridging branch of the structure of Fig. 20 may be made partly balanced and partly unbalanced; and

Fig. 22 is a modification of the network of Fig. 21 in which the ideal transformer has been eliminated.

One general form of the network of the invention is represented diagrammatically by the symmetrical lattice structure of Fig. 1, which comprises a pair of equal line impedances Za and a pair of diagonal impedances Zb connected between a pair of input terminals I, 2 and a pair of output terminals 3, 4. Only one line impedance Z8. is shown, the one connected between terminals 2 and 4 being indicated by the dotted line, and in like manner the dotted line connecting terminals 2 and 3 represents a second diagonal impedance branch Zb. A source of electromotive force E is shown in series with the load impedance Z5 connected to the input terminals, and the impedance Zr represents the load connected to the output terminals. The impedances Z5 and Z: may represent, for example, sections of transmission line or other terminal loads of suitable impedance.

The line, impedance branch Za comprises a plurality of partial networks F1, F2 F11 connected in series at one end. The diagonal branch Zb is made up of a like number of partial networks F1, F2 F11 connected in parallel. The partial networks forming the line impedance branch may, if desired, be connected in parallel, in which case the corresponding partial filters in the diagonal impedance branch will be connected in series. Or, again, the line branch may be made up of a number of partial networks connected in series together with other partial networks connected in parallel, so long as the diagonal branch contains their inverse structures, connected in inverse relationship. Each partial network may, for example, be a four-terminal wave filter comprising any number of component sections, which may be all of the same type or may be of different types. The distant end of each of these partial networks is terminated in a resistance chosen to match the characteristic impedance of the network as nearly as possible.

The partial filters F1 and F1 are so designed that the product of the impedance Z1 looking into the input terminals of F1 times Z1, the impedance looking into the input terminals of F1, is a constant quantity at all frequencies. This can be accomplished by making the filter F1 an inverse structure with respect to the filter F1. Each of the other partial networks connected in series in the Za impedance branch likewise has its inverse structure connected in parallel in the Zb impedance branch. It follows, therefore, that the product of the impedance of the line branch Za times the impedance of the diagonal branch Zb will be a constant quantity at all frequencies, and therefore the characteristic impedance K of the lattice structure at terminals I, 2 and 3, 4, which is given by the equation K= /Z,,Z,, will also be a constant quantity at all frequencies, both within and without the transmission band of the network as a whole.

The propagation constant P of the network of Fig. 1 is given by the expression An inspection of Equation (2) shows that in the regions where Z3. and Zb are of the same sign,

P t h-= tanh is real and therefore the structure attenuates the energy passing through it, and where Z3. and Zb are purely reactive but of opposite sign,

tanh

will be substantially pure non-reactive impedances of the same sign, and therefore P tanh is real. networks are attenuating, the impedances Zn and Zb are substantially only reactive and of opposite sign, and therefore the structure as a whole will transmit freely the frequencies lying within this region. To summarize, the lattice network of a:

Fig. 1 will have its transmission band located where the partial networks have attenuation bands, and the network as a whole will have attenuating regions located where the transmission bands of the partial networks occur.

Since the characteristic impedance of the network of Fig. 1 is a constant pure resistance at terminals I, 2, and 3, 4, there must be a dissipative load to absorb the incoming energy at all frequencies. In the transmitting bands of the network as a whole the energy supplied by the source E is dissipated in the load impedance Zr. In the attenuating bands of the network as a whole, which correspond to the transmitting bands of the partial filters, this energy is dissipated in the terminating resistances R1, R2 R11 and R1, R2. R11. There will, therefore, be transmission bands between terminals I and 2 and the terminating loads of the partial networks and also corresponding transmission bands from On the other hand, where the partial Y F1, F2

which is the same as that of the corresponding the terminals 3 and 4 to the same terminating loads. As will be fully explained hereinafter the output energy from these various partial networks may be combined and in this way a plurality of transmission channels may be provided having characteristic impedances which are constant pure resistances at all frequencies.

A second form of the invention is shown in the bridged-T network of Fig. 2, which is the electrical equivalent of the lattice structure shown in Fig. 1. The network of Fig. 2 has a bridging branch comprising the partial filters F1, F2 F11 connected in series at one end, and a shunt branch comprising the inverse partial filters F1, F2. F11 connected in parallel. The bridging branch may, of course, consist of parallel connected partial filters, and the shunt branch of series connected partial filters. The two impedance branches are coupled by means of a socalled ideal transformer Ta having three windings of large self-inductance and close coupling. The primary comprises two equal windings W1 and W1 connected series aiding with mutual inductance M1 efiective between them equal to the self-inductance of each winding. The secondary consists of a third winding W2 which is equal in inductance to A1(W1+W1') and is coupled to the primary by mutual inductance The transformer Ta will have a 4:1 impedance ratio between primary and secondary. By means of Bartlett's bi-section theorem given in the Philosophical Magazine, (London) vol. 4, page 902, November 1927, it may be shown that the bridged-T network of Fig. 2 is the electrical equivalent of the lattice structure shown in Fig. 1, and therefore the bridged-T network will have the same transmission and attenuation channels described above in connection with Fig. 1.

The partial filters in the bridging branch of the bridged-T network are designed on the basis of a characteristic impedance equal to one-half that of the corresponding filters in the line branch of the lattice network and therefore the bridging branch of the bridged-T structure will have a total impedance equal to Ze. Also the shunt branch of the bridged-T structure will have component partial filters which have characteristic impedances equal to one-half of the characteristic impedance of the corresponding networks in the diagonal branch of the lattice structure shown in Fig. 1, and therefore the total impedance of the shunt branch of the bridged- T network will be 210. The partial networks in the bridging branch of the bridged-T network are terminated respectively in the resistances /zR1, A2552 /2Rn and the corresponding inverse filters in the shunt branch are terminated respectively in the resistances R1, R2. /gRn.

A modified form of the bridged-T network of Fig. 2 is shown in Fig. 3, in which the coupling transformer Ta is replaced by n coupling transformers T1, T2 Tn, one associated with each partial filter in the bridging branch. These coupling transformers are of the so-called ideal type described above and have an impedance ratio of 1:1. The primary windings are all connected in series, with a partial filter connected to each primary, and the secondary windings are also connected ,inseries. The partial filters F11 'have a'characteristic impedance partial filters in the bridging impedance branch of the network of Fig. 2 and these filters are terminated, respectively, in the resistances R.1, /2R.2 /gRn. The shunt branch of the modified bridged-T network of Fig. 3 is identical with the shunt branch of the network of Fig. 2. When the partial networks F1, F2 F11 have initial impedance branches which comprise shunt inductances, the ideal transformers T1, T2 Tn may be replaced by transformers having finite winding inductances, as will be fully explained hereinafter.

When the partial filters F1, F2 F11 of the bridging branch of the network of Fig. 2 are, for example, band-pass filters and the corresponding networks F1, F2. F11 in the shunt branch of the network are inverse structures passing the same bands of frequencies, respectively, as the corresponding partial filters in the bridging branch, the output energy from the various partial filters may be combined as shown in Fig. 4 to provide a plurality of separate transmission channels. If K is the characteristic impedance of each of the partial filters F1, F2

F11, and K is the characteristic impedance of the partial filters F1, F2. F11 these two quantities must satisfy the equation K I II.- KK 4 In every case, however, all of the terminating impedances of the partial filters are equal to each other, and each is equal to i 2 In equation form,

a n a a 5 (5) The terminating impedance of the partial filter F1 may now be connected in series with the terminating impedance of the partial filter F1, as shown in Fig. 4, to form a band-pass channel between terminals I, 2 and terminals 5, 6', as will be more fully explained below in connection with a specific example. The output terminals 5' and 5 of the partial filters are connected directly together. The energy outputs from the other partial filters may be combined in like manner to form additional transmission channels, the number of possible channels corresponding to the number of pairs of partial networks.

In the network shown in Fig. 4. the characteristic impedance looking in at the output terminals of the various channels will not be a constant 1 pure resistance at all frequencies, but may be made so by resorting to the construction shown in Fig. 5. The network of this figure requires the addition of a three-winding ideal transformer having an impedance ratio of 1:1 in each separate channel. The two output impedances :R1 and R1 are connected in series across the secondary of the transformer T1 in the first channel. One output terminal of the partial filter F1 is connected to the junctionpoint between the two impedances .just mentioned and the other output terminal of F1 is connected to the mid-point of the divided secondary winding of thetransformer T1. In Fig. 5 the ideal transformer Tb has an impedance ratio of 151, and thepartial filters F1, F2 F11 are designed on the basis of a characteristic impedance K equal to 2K. With this construction, the network will have a characteristic impedance at each pair of terminals which is a constant pure resistance at all frequencies.

Certain of the partial networks of Fig. 4 may beonly two-terminal impedances which may contain dissipative elements or may comprise only reactances. As shown in Fig. 6, for example, the bridgingbranch is made up of a partial filter F1 and the twotwo-terminal i'npedances N1 and N2 connected in parallel. The shunt branch consists of the-inverse networks F1, N1 and N2 connected in series. Theseauxiliary-two-terminal networks may be used for the purpose of increasing the attenuation in the various channels at the crossover frequencies, as will be explained by means of an example hereinafter.

A number of more specific embodiments of the invention will now 'be described as illustrative examples. An example of the lattice structure of Fig. 1 is shown in Fig. 7, in which each line impedance branch consists of the two partial filters F1 and F2 connected in series and each diagonal impedance branch is made up of the inverse structures F1 and F2 connected in parallel. More than two partial filters may be used in each impedance branch and each partial filter may comprise any number of sections either of the same kind or of different types.

In Fig. '7 all of the partial filters are of the high-pass type, with the cut-off frequency placed at fc. The network as a whole, therefore, will have a characteristic impedance at terminals l, 2 and also at terminals 3, 4 which is a constant pure resistance at ail frequencies. Furthermore, the network will have a low-pass transmission channel between terminals I, Z and 3, 4 which will freely pass all frequencies lying between zero and 111. The attenuation in this channel will depend upon the balance between the impedances of the branches Z2. and Zh- In accordance with the invention the partial filters are so designed that the impedances Z3. and Z1) are made equal to each other throughout the transmission bands of the partial filters. If a sufficient number-of partial filters are used and each partial filter is composed of an infinite number of sections this equality can-be'made exact, and as a result the attenuation of the network as a whole will be infinite vover the entire attenuating region.

Even if-each impedance branch consists of only two single-section partial filters, as shown in Fig. I, by proper design, this condition of equality may be closelyapproximated and a sustained high attenuation may be provided. In Fig. 7 the partial filter F1 is a single-section, constant-k type, high-pass filter with mid-series termination at each end. The design parameters for this filter are the cut-off frequency fc and its characteristic impedance K, which is equal to where K is the characteristic impedance of the network as a whole. The filter comprises two equal series capacitances C1 and an interposed shunt inductance L1. The inverse structure F1 in the diagonal branch of the network is a singlesection, mid-shunt terminated, constant-k, highpass filter having two shunt inductances L2 and an'interposed series capacitance C2. The design parameters for this filter are the cut-ofi fc and the characteristic impedance K" which is equal to The partial filter F2 is a mid-series terminated, shunt-derived, m-type section in which the peak of attenuation occurs at a frequency slightly below the cut-off frequency. Each series branch of the-filter comprises an inductance L3 in parallel-with the capacitance C3 and the shunt impedance branch consistsof the inductance L4.

fhe partial filter-F2 which comprises the inverse structure located in the diagonal impedance branch-is a mid-shunt terminated, series-derived, m-type section, the characteristic impedance of which is equal to 2K. Each shunt branch-consists of a capacitance C5 in series with an inductance L5, and the interposed series branch is constituted by the capacitance C4.

If each partial filter has an infinite number of sections, the best results will be obtained by making the partial filter F1 of the constant-k type (in which m=l) and designing the m-derived partial filter F2 on the basis of an m equal to about 0.332. As the number of sections is reduced the value of these ms should also be decreased. This may be done by decreasing the m of the filter F1, that is, by making this filter an m-derived type in which 172 is less than unity, or by decreasing the m of the filter F2, or by decreasing the ms of both of these filters.

When terminated in a resistance /?R. equal to /2K the filter F1 will have an input impedance which has aresistive component 11 of the type shown by curve I of Fig. 8, which starts at zero at the cut-off frequency fc and rises to a, value K at infinite frequency. In the same region the impedance of the filter F2 will have a resistive component T2 of the form shown by curve 2 of Fig. 8, which starts at zero at the cut-off frequency, rises-to a maximum and then falls to a value K at infinite frequency. The sum of the. curves l and 2 is shown by the curve 3 which, it will be noted, very soon after the cut-off frequency rises to a value K, from which it deviates only slightly between that frequency and infinite frequency. The curve cuts the K line at the frequencies f1 and f2. The impedance of the Z11 branch .will .be equal to K at these same frequencies and therefore attenuation peaks will occur at these frequencies as well as at infinite frequency, as shown by the typical attenuation characteristic of Fig. 9. Between these attenuation peaks theattenuation curve will maintain a constantly high value since the impedances of the branches Za and Zb deviate but slightly from equality throughout this entire frequency range.

A specific embodiment of the network of Fig. 5 is shown in the network of Fig. 10, which is a band-pass filter having three separate channels. The bridging impedance branch comprises three partial filters F1, F2 and F3 connected in series at one end, and the .shunt branch comprises the inverse structures.F1,'F2 and F3 connected in parallel. The filters F1, F2 and F: are unbal- 7 anced, mid-shunt terminated, constant-k, bandpass filters designed on the basis of a characteristic impedance equal to 2K and having their transmission bands spaced as desired. The partial filters may have the transmission characteristics shown, respectively, by curves 4, 5 and 6 of Fig. 11. At the two cross-over points is and f4 the attenuation may be made any desired amount either by proper spacing of the individual channels or by increasing the number of sections in each partial filter.

The principal transmission paths in the multiband multi-channel constant resistance filter cf Fig. 10 are shown diagrammatically in Fig. 12. Energy applied to terminals I, 2 falling within the transmission bands of the partial filters will be transmitted to the loads connected, respectively, to the terminals 5, 6, the terminals 1, 8 and the terminals 9, 10 as indicated by the solid line arrows A, B and C in the figure. The transmission characteristics of these channels will be determined by the propagation constants of the partial filters and will be of the type shown by the curves of Fig. 11, modified slightly due to the presence of the associated partial filters. Energy applied to terminals 1 and 2 which falls between and outside of the channels just described will be dissipated in the load connected to terminals 3 and 4 and therefore between these two sets of terminals there will be a multi-channel band-pass characteristic in which the transmitted bands correspond with the attenuated regions of the partial filters. On the other hand, if energy is applied to terminals 3, 4 that part which falls within the transmission bands of the partial filters will be freely transmitted to the loads connected respectively to the terminals 5, 6', terminals 1', 8' and terminals 9', It? as shown by the dotted line arrows A, B and C, while the energy falling between and outside of these bands will be transmitted to the load connected to terminals I and 2. There will also be a transmission path between terminals 5, 6 and terminals 5', 6 for the frequencies passed by the partial filter F1 as shown by the arrow A" in Fig. 12, and there will be similar paths for the frequencies passed, respectively, by the partial filters F2 and F3 as indicated by the arrows B and C. When each of the connected loads of Fig. 10 is a resistance equal in value to K the characteristic impedance at each pair of terminals will be a constant pure resistance at all frequencies.

The network of Fig. 10 is well adapted for use in a communication system to separate the carrier frequencies into their separate channels. The line carrying all of the frequencies may, for example, be connected to terminals 1 2 and three channels connected respectively to terminals 5, 6, terminals '5, 8 and terminals 9, It. Resistances equal in value to K are connected respectively to the other pair of terminals. The transmission channels A, B and C of Fig. 12 may then be utilized to separate the incoming frequencies into their respective channels.

The attenuation in channel A may be increased by the addition of an auxiliary filter F1, between the terminals 5 and 6 and the connected load rep= resented by R1 as shown in Fig. 13. This auxiliary filter is effective only in channel A and by means of it the attenuation in this channel may be increased to any required extent. If the filter F1" is itself a constant-resistance structure, that is, one having a characteristic impedance K which is a constant pure resistance at all frequencies,

the constant resistance properties of the main network will not be disturbed thereby. Similar auxiliary filters F2" and F3" may be introduced, respectively, into the channels B and C as shown diagrammatically in Fig. 13.

If it is not required that all of the channels have a constant resistance characteristic impedance, the network of Fig. 10 may be modified as shown by the network of Fig. 1 1, in which the resistances R1, R2 and R3 have been eliminated and the three-winding transformers T1, T2 and T3 have been replaced by the two-winding transformers T1", T2 and T3" having a unity impedance ratio. This network will have the transmission paths indicated by the arrows A, B, C and A, B, C in Fig. 12. The characteristic impedance at terminals 5, 2 will be a constant pure resistance at all frequencies but at terminals 5,

terminals 1, 8 and terminals 9, Hi the characteristic impedance will be similar to that of the respective partial filters F1, F2 and F3, but will be more constant within the. transmission bands. The network of Fig. 14 follows the general type of that shown in Fig. 4. In Fig. 14 the ideal transformer Ta has an impedance ratio of 4:1 and the partial filters F1, F2 and F3 are designed on the basis of a characteristic impedance K equal to A modified bridged-T network of the type represented by Fig. 3 is shown in Fig. 15 having three partial filters F1, F2 and F3 in the bridging branch and the corresponding inverse filter structures F1, F2 and F3 in the shunt branch, the two impedance branches being coupled by means of the three transformers T1, T2 and T3. The partial filters are of the same type as those described in connection with Fig. 14. The primary of the ransformer T1 is formed by the initial shunt inductance of the partial filter F1. This transformer has a 1:1 impedance ratio and therefore its secondary winding has a self-inductance equal to that of the primary, assuming perfect coupling. The coupling transformers T2 and T3 are formed in a similar manner and thus no transformers of the ideal type are required in the construction of this network. The output transformer T1 has its primary winding formed by the final shunt inductance of the partial filter F1. This transformer has an impedance ratio of 1:4 with a divided secondary winding tapped at the mid-point as shown. The other two output transformers T2 and T3 are constructed in a similar manner. The network will have the same transmission paths as those shown in Fig. 12 and will have a characteristic impedance at each pair of terminals which is a constant pure resistance at all frequencies.

If it is not necessary that the characteristic impedance of all the channels be a constant pure resistance at all frequencies, the network of Fig. 15 may be modified as shown in Fig. 16, in which the three-winding transformers T1, T2 and T3 are replaced by the two-winding transformers T1", T2" and T3" having impedance ratios of 1:1. This network will have a constant resistance characteristic impedance at terminals I, 2 but at terminals 5, 6, terminals 7, 8' and terminals 9, H) the characteristic impedance will be that of a constant-k type band-pass filter but will be somewhat more uniform in the transmission band.

A specific example of the network of Fig. 6 is shown-in Fig. 17. Thebridgingbranchcomprises a dissipative two-terminal auxiliary impedance N and a four-terminal partial'filter F connected lnzparallel. The corresponding inverse structures N and F are connected in series in the shunt im- .pedance branch. The partial filter F is a singlesection, high-pass filter of the m-derived type ihaving a mid-shunt termination at each end. *Each shunt impedance branch consists of an inductance Lb, and the interposed series branch comprises an inductance La and a capacitance Ca connected-in parallel. The filter is designed on the basis of a characteristic impedance equal to K. .I'he cut-01f frequency fciand the peak of atl5 tenuation,'which occurs .at the. frequency is, are placedasrequired. The filter F is a high-pass filtercf inverse structure and has a characteristicimpedanceK" related to K by the expression awhere Kris the characteristic impedance of the networkias azwholeaat terminals: I and 2. "The impedance'K' may be chosen equal to or it may be given a value either larger or smaller than this. Once K ist-detelmined, the value of K" is found from the above equation.

The auxiliary network N in the bridging branch consists ofzaniin'ductance L ra capacitance CN and a; resistance Rmall connected in series with each other and in parallel with the filter F. The

"inductanceLN'and thecapacitance. CN are designed to resonate at a frequency slightly above :the cut-01f fc of the filter F, as will be explained more; fully below. The inverse auxiliary network N"comprises an inductancelm', a capacitance 40 "cifand airesistance RN connected in parallel with'eachother'and in .series with the partial filter F. When the elements inv the network N *havebeennetermined the values of the elements in the inverse structure N may be found from the relationship -In Fig. 17- the bridging impedance branch is '50 coupled --to the shunt impedance branch by means of the transformer T4 which has-a divide'd primary winding and-an impedance ratio of-4z1- between primary and secondary. The secondary winding is the' inductance Lb, which, also '55 constitutesa shunt inductance of the partial filter-F,-and thus only finite winding inductances are-required for the transformer T4.

*If the partial 'filterF" has a characteristic impedance equal to- K the resistance component G0 13 in the transmission range will be of the form --'shownby the dotted line curve'lof Fig. 18, starting from zero at the cuto'ff frequency In and rising to a value equal -to- K at infinitefrequency. '-'If the auxiliary networks N and N are omitted,

the network as awhole will have a low-pass transmission'channel between terminals I,2 and ter- -minals 3,= 4-of= the form indicated by the dotted 'line curve-8- of Fig. 19, dependent upon the impedancematchbetween the bridging and shunt '70 "branches and rising to an infinite value at infrequency is and rising again toan infinite value attenuation A1 is approximately 3 decibels.

at zero frequency. Thesetwo curvescross each other at the frequency fx, at which point the The cross-overpoint fx'Wlll occur approximately at the cut-off frequency fc.

By the addition of the auxiliary networks N and N the attenuation at the cross-over point .may be increased to any desired value, and one or-more peaks of attenuation may be introduced line at thefrequencies'fiand fa. The low-pass channel will now have peaks of attenuation at these two frequencies, as shown. by the solid line curve I2 ,of Fig-19, and the attenuation of the high-pass channel will be slightly modified as indicated'bythe solidline curve i3. The two curves will now cross each other at the frequency Ix, at

which point the attenuation is increased from A1 toa new valueAz. In this way the attenuation in the low -passchannel is sharpened above the cut-off and the attenuation .at the cross-over point may be made any required amount.

Fig. 20 shows anetwork of the bridged-T type in which the bridging branchcomprises a single .full section of a shuntrderived, m-type, highpass filter-Fa terminated mid-series at each end, and theshunt branch consists of a filter Fa which has the inverse-structure of the filter Fa. The filter Fa consists of a full'section of the seriesderived, m-type terminated mid-shunt atboth ends. Filters Fa and Fe are both high-pass filters having the cut-off frequency chosen as required. The filter Fa is couple-d to the filter Fa by means. of the transformer Ta which is of the ideal type and has an impedance ratio 4:1, the primary beingdivided into two equal windings.

The outputs of the filters Fa and Fe are connected inseries to form a high-pass transmission channel between terminals I, 2 and terminals 5, 6. There will ralso-be a low-pass channel between terminals I, 2,.and terminals 3, 4. The network will have a characteristic impedance at terminals I and 2 which is a constant pure resistance at all frequencies-butat terminals 3, 4 and terminals 5,.6 it will not be,-a constant resistance structure.

The first impedance branch of the filter Fa comprising the inductance La and the capacitance Csmay be divided into two equal portions, one of which is placed in the other side of the line as shown inFig. 21. The filter Fe. is thus made partly balanced and partly unbalanced, that is to say, it comprises a half section of the balanced type and a half. section of the unbalanced type.

It will benoted that the secondary of the transformer Te has connected across it the three inductances /zLe, L7 and Ls. In accordance with the invention, transformers may be substituted for these three inductances and the ideal transformer'Ta eliminated. Fig. 22 shows how this may be done. The inductance L7 is divided into two equal portions each equal to L1 with a mutual inductance M3 equal to L'1 eifective therebetween. Likewise the two inductances A LG and Ls are coupled by mutual inductance M4 equal to /2116. The network of Fig. 22 will have the same transmission characteristics as the networks of Figs. and 21, but as pointed out the transformers employed require winding inductances of only finite value.

What is claimed is:

1. In a multi-channel wave transmission network comprising a plurality of impedance branches, two impedance branches adapted to determine the transmission characteristics of the network, one of said impedance branches comprising a plurality of partial networks, the other of said impedance branches comprising a plurality of other partial networks having structures which are inverse with respect to said first-mentioned partial networks, and the output of each of said partial networks in said one branch being combined with the output of said corresponding partial network in said other branch to provide a separate transmission channel.

2. In a multi-channel wave transmission network having a plurality of impedance branches, two impedance branches adapted to determine the transmission characteristics of the network, one of said branches comprising a plurality of partial filters connected in series at their input terminals, the other of said branches comprising a plurality of other partial filters connected in parallel at their input terminals, the structure of one of said branches being inverse with respect to the structure of said other branch, and the product of the impedances of said two branches being at all frequencies a constant real quantity equal in magnitude to the square of the characteristic impedance of said transmission network.

3. In a multi-channel wave transmission network having a plurality of impedance branches, two impedance branches adapted to determine the transmission characteristics of the network, one of said branches comprising a plurality of partial filters connected in series at their input terminals, the other of said branches comprising a plurality of other partial filters connected in parallel at their input terminals, and the product of the impedances of said two branches being a constant quantity at all frequencies.

4. A wave transmission network having a plurality of pairs of. terminals, a plurality of transmission channels, and two branches adapted to determine the transmission characteristics of the network, the characteristic impedance at each of said pairs of terminals being a constant pure resistance equal to K at all frequencies, one of said branches comprising a plurality of partial filters connected in series at their input terminals, the other of said branches comprising a plurality of other partial filters connected in parallel at their input terminals, and each of said partial filters in said one branch being so proportioned with respect to a filter in said other branch that the product of their impedances is a constant quantity equal to K at all frequencies.

5. A selective wave transmission network of the lattice type having a pair of input terminals and a pair of output terminals, said network com prising a line impedance branch connected between an input terminal and an associated output terminal, and a diagonal impedance branch connected between said input terminal and the other of said output terminals, said line branch comprising a plurality of four-terminal partial filters connected in series at one end, said diagonal branch comprising an equal number of other four-terminal partial filters of inverse structure with respect to said partial fiiters in said line branch connected in parallel at one end, each of said partial filters being terminated in a resistive load impedance, and the product of the impedance of said line branch multiplied by the impedance of said diagonal branch being a constant quantity at all frequencies.

6. A multi-channel selective wave transmission network of the bridged-T type comprising a bridging impedance branch and a shunt impedance branch, said bridging branch comprising a plurality of partial filters, said shunt branch comprising a plurality of other partial filters, the output of each of said partial filters in said bridging branch being combined with the output of a corresponding partial filter in said shunt branch to provide a separate transmission channel, and the product of the impedance of said bridging branch multiplied by the impedance of said shunt branch being a constant quantity at all frequencies.

'7. A multi-channel wave transmission network of the bridged-T type comprising a bridging impedance branch consisting of a plurality of partial filters, and a shunt impedance branch consisting of a plurality of other partial filters of inverse structure with respect to said first-mentioned partial filters, said bridging branch being inductively coupled to said shunt branch by means of a three-winding transformer, the output of each of said partial filters in said bridging branch being combined with the output of said corresponding partial filter in said shunt branch to provide a separate transmission channel, and the impedance of said network being constant in magnitude and non-reactive in character at all frequencies.

8. A wave transmission network having a pair of input terminals and a pair of output terminals, said network comprising an impedance path between an input terminal and an associated output terminal, a plurality of transformers having their primaries connected in series between said input terminal and the mid-point of said impedance path, and their secondaries connected in series between said mid-point and said output terminal, a plurality of partial filters connected, respectively, to said primaries, and a shunt impedance branch connected on one side to said mid-point and on the other side to said remaining input and output terminals, said shunt branch comprising a plurality of other partial filters, and said partial filters in said shunt branch having structures which are inverse with respect to said first-mentioned partial filters.

9. A multi-channel wave transmission network of the bridged-T type comprising a bridging impedance branch and a shunt impedance branch inductively coupled by means of a transformer, said bridging branch comprising a plurality of partial filters, said shunt branch comprising a plurality of other partial filters having structures which are inverse with respect to said first-mehtioned partial filters, and the output of each of said partial filters in said bridging branch being combined with the output of said corresponding partial filter in said shunt branch to provide a separate transmission channel.

10. A multi-channel wave transmission network of the bridged-T type comprising a bridging impedance branch and a shunt impedance branch inductively coupled by means of a transformer, said bridging branch comprising a plurality of partial filters, said shunt branch comprising a plurality of other partial filters having structures which are inverse with respect to said first-mentioned partial filters, and the output of each of said partial filters in said bridging branch being combined by means of a three-winding transformer with the output of said corresponding partial filter in said shunt branch to provide a separate transmission channel having a characteristic. impedance which is a constant pure resistance at all frequencies.

, 11. A multi-channel wave transmission network of the bridged-T type comprising a bridging impedance branch and a shunt impedance branch inductively coupled by means of a three-winding transformer, said bridging branch comprising a partial filter and a dissipative network, said shuntbranch comprising a second partial filter and a seconddissipative network, the structure of said shunt branch being inverse with respect to the structure of said bridging branch, and the output of said first partial filter being combined with the output of said second partial filter to form a transmission channel.

12.- A wave transmission network of the lattice type comprising a line impedance branch and a diagonal impedance branch, each of said impedance branches comprising a plurality of partial filters having the same cut-off frequency, the partial filters in one of said branches having a structure which is inverse with respect to the structure of said partial filters in said other impedance branch, and the impedance of each of said branches being substantially a constant pure resistance throughout the entire transmission band of said partial filters.

13. A wave transmission network of the bridged-T type comprising a bridging impedance branch and a shunt impedance branch, said bridging branch comprising a plurality of partial filters, said shunt branch comprising a plurality of other partial filters having a structure which is inverse with respect to said partial filters comprising said bridging branch, the output of each of said partial filters in said bridging branch being combined with the output of said corresponding filter in said shunt branch by means of a transformer to provide a separate transmission channel, and one winding of each of said transformers constituting a shunt inductance element of the partial filter with which said transformer is associated.

14. A wave transmission network of the bridged-T type comprising a bridging impedance branch and a shunt impedance branch inductively coupled by means of a three-winding transformer, said bridging branch comprising a plurality of band filters adapted to pass different transmission bands, said shunt branch comprising aplurality of filters having structures which are inverse with respect to said first mentioned filters, and the output of each of said filters in said bridging branch being combined with the output of the corresponding filter in said shunt branch by means of a transformer to provide a separate transmission channel.

15. A wave transmission network having an impedance path comprising a plurality of transformers having their primary windings and their secondary windings connected respectively in series between an input terminal and an output terminal, a shunt branch comprising a plurality of partial filters connected to the mid-point of said impedance path, and a plurality of other partial filters of inverse structure connected respectively to the primaries of said transformers, the output of each of said last-mentioned filters being combined by means of a three-winding transformer with the output of the said corresponding filter in said shunt branch to form a separate transmission channel having a characteristic impedance which is a constant pure resistance at all frequencies,

16. A wave transmission network having a pair of input terminals and a pair of output terminals, said network comprising an impedance path connected between an input terminal and an associated output terminal, and a shunt impedance path having connections on one side to the midpoint of said first-mentioned path and connections on the other side of each of said remaining terminals, said first-mentioned path comprising a plurality of transformers having their primary windings connected in series between said input terminal and said mid-point and having their secondary windings connected in series between said mid-point and said associated output terminal, and a plurality of band filters adapted to pass difierent transmission bands connected respectively to the primary windings of said transformers, said shunt impedance path comprising a plurality of filters having structures which are inverse with respect to said first-mentioned partial filters, and the output of each of said firstmentioned partial filters being combined with the output of said corresponding filter in said shunt path by means of a transformer to provide a separate transmission channel.

1'7. A multi-channel wave transmission network having a pair of input terminals, a pair of output terminals, and impedance paths connecting each of said input terminals with its associated output terminal, said network comprising a partial filter connected at one end between the mid-point of one of said paths and a point in the other of said paths, and a second partial filter having a structure which is inverse with respect to said first-mentioned partial filter, said second partial filter having an initial balanced half section of the ladder type comprising a pair of equal series inductance inductively coupled with unity coupling factor followed by an adjacent shunt branch comprising a second pair of equal inductances also coupled with unity coupling, all of said inductances being connected in series in one of said impedance paths, and the outputs of said partial filters being combined to provide a separate transmission channel.

18. A wave transmission network of the bridged-T type comprising a bridging branch and a shunt branch inductively coupled, said bridging branch comprising a partial filter and a dissipative network, said shunt branch comprising a second partial filter and a second dissipative network, the structure of said shunt branch being inverse with respect to the structure of said bridging branch, the output of said first partial filter being combined with the output of said second partial filter, said transmission network having two contiguous transmission channels, and said dissipative networks being so designed as to increase the atenuation at the cross-over point between said two transmission channels.

19. A wave transmission network of the bridged-T type having a pair of input terminals and two pairs of output terminals, said network comprising a bridging branch and a shunt branch inductively coupled, said bridging branch comprising a partial filter and a dissipative network, said shunt branch comprising a second partial filter and a second dissipative network, the structure of said shunt branch being the inverse of the structure of said bridging branch, said transmission network having a transmission channel between said input terminals and a pair of said output terminals the attenuation of which is dependent upon the impedance balance between said bridging branch'and said shunt branch, the outputs of said partial filters being combined to provide a second transmission channel between said input terminals and the other'fpair oi! said output terminals the attenuation of which is dependent upon the propagation constants of said partial filters, and said dissipative networks being adapted to steepen the slope of the attenuation of said first-mentioned channel near the cutofl frequency.

STEPHEN BOBIB. 

